For P a poset or lattice, let Id(P ) denote the poset, respectively, lattice, of upward directed downsets in P, including the empty set, and let id(P ) = Id(P )−{∅}. This note obtains various results to the effect that Id(P ) is always, and id(P ) often, “essentially larger” than P. In the first vein, we find that a poset P admits no <-respecting map (and so in particular, no one-to-one isotone...

This paper shows that any compactly generated lattice is a subdirect product of subdirectly irreducible lattices which are complete and upper continuous. An example of a compactly generated lattice which cannot be subdirectly decomposed into subdirectly irreducible compactly generated lattices is given. In the case of an ideal lattice of a lattice L, the decomposition into subdirectly irreducib...

This paper deals with the formation control of a group of point masses subject to ideal Coulomb friction. We propose a discontinuous controller which provides a solution to the exact formation problem in the presence of ideal Coulomb friction.

The quantum-event / prime ideal in a category/ noncommutative-point alternative to classical-event / commutative prime ideal/ point is suggested. Ideals in additive categories, prime spectra and representation of quivers are considered as mathematical tools appropriate to model quantum mechanics. The space-time framework is to be reconstructed from the spectrum of the path category of a quiver....

Exploiting the analogy between exemplar models and population coding schemes, we characterize, by means of information theoretic tools, the efficiency of a large but finite population of cells coding for a discrete set of categories (e.g. vowels). The optimal code is shown to typically allocate more cells to class boundaries than to regions further apart. We then discuss the predicted perceptua...

We consider the problem of designing reliable and confidential lattice codes, known as wiretap lattice codes, for fast fading channels. We identify as code design criterion for finite lattice constellations a finite sum of inverse of algebraic norms, in fact the analogous for finite sums of the known criterion for infinite constellations, which motivates us to study totally real number fields w...

Pregnancy and delivery is one of the main causes in the female body weight alteration, especially with obesity. This alteration in body weight has a significant effect not only for a femine beauty standpoint, but also for more important reproductive functions in postpartum. For the actual condition of the maternal body weight alteration and its clinical significance, we made the various analysi...

BACKGROUND AND PURPOSE The American Heart Association developed the ideal cardiovascular health (CVH) index as a simple tool to promote CVH; yet, its association with brain atrophy and dementia remains unexamined. METHODS Our aim was to investigate the prospective association of ideal CVH with vascular brain injury, including the 10-year risks of incident stroke and dementia, as well as cogni...

Supply chain risk evaluation is a multi-criteria decision making problem under fuzzy environments. To tackle the problem, this paper firstly identifies and discusses some of the important and critical decision criteria and constructs the evaluation indicator framework. Then this paper presents a modified grey relational analysis method based on the concepts of ideal and anti-ideal points. In th...

The Circumplex Scales of Interpersonal Values (CSIV) is a 64-item self-report measure of goals from each octant of the interpersonal circumplex. We used item response theory methods to compare whether dominance models or ideal point models best described how people respond to CSIV items. Specifically, we fit a polytomous dominance model called the generalized partial credit model and an ideal p...